Yes, most
definitely. Some older phones will have been supplied with a
rechargeable NiCd
battery but you can certainly use a NiMH battery to replace it. If you
were to buy the same phone again today it would almost certainly be
supplied with a rechargeable NiMH equivalent.

My
existing battery has a lower mAh rating than the battery showing on your
website. Is this OK?

Yes, most
definitely. mAh is simply a measure of a batteries capacity and if the
battery you see has a higher rating then it's fine. All this means is that you will
enjoy longer talk/standby times due to the increased capacity of the
rechargeable battery.
Occasionally the replacement battery we supply will have a slightly
lower rated capacity. Again, the battery will work perfectly in your
telephone and you will probably not notice any difference whatsoever.